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V wind, pixel size and map factors



I'm currently working on Tahiti Island in French Polynesia (approximately bounded by 154°W / 13°S to 145°W / 22°S) using the Mercator projection.

I'm a bit lost. I've been reading about map factors in Skamarok et al., 2008 (working with WRF V3.6) and in the corresponding version of the User's Guide, but I haven't been able to find answers to my questions. For example:

1) When post-processing wind data, do I need to correct the V component based on latitude (map projection)? If so, how should I do this? What about V10?

2) Similarly, for grid-averaged data like T2, etc., how should I post-process my data to account for the "pixel size" of a given grid cell? Is the weighting correction VARIABLE*cos(lat) sufficient? Or shall I use grid-cell's map-factor coefficient ?

Thank you in advance for any assistance you can provide.